Problem is if it's a separate program that is installed with a game an uninstaller tool isn't going to be able to also remove it along with uninstalling the game in one go - they'd need to have separate uninstall programs with them.
One suggestion is to install an installation watching program; i.e.; Total Uninstall (there's a Last Freeware Version, but it might not work correctly on modern Windows OSes), ZSoft Uninstaller (freeware), etc., there's other freeware tools that do the same. You'd run the built-in uninstaller from Windows Add/Remove (or whatever it's called nowadays), then you'd have Total Uninstall, ZSoft Uninstaller, etc., remove the left-overs using them. Never use such tools to uninstall drivers however as they will cause only problems that may cripple the system.
Or do your software installs and uninstalls with something like the paid version of Revo Uninstaller Pro, it can watch installations and then later uninstall them. Again I wouldn't recommend uninstalling drivers with it!
If you wish to do everything the freeware route you can do software uninstalls with Revo Uninstaller Free, but it won't know exactly what was done during install it's more a look for left-overs and it may miss some things but it's better than using the Windows Add/Remove which never looks for left-overs.
Here's how I do it for free in this precise order from install to uninstall (not with drivers however I only use Windows Add/Remove for drivers):
1. Total Uninstall (Last Freeware Version), pre-scans the system before an install.
2. Install the software. Use the software for several minutes so it creates settings, and possibly junk files like logs, etc.
3. Return to Total Uninstall (Last Freeware Version), it now scans the system for differences after the install.
Should I want to uninstall the program:
1. Uninstall with Revo Uninstaller Free. And reboot if necessary.
2. Total Uninstall (Last Freeware Version), using the saved scanning results I have it remove all known left-overs.
Note this is not a 100% guaranteed way to remove everything, still some manual removal is necessary depending upon the program that was uninstalled such as antivirus, etc.